A note for a second order periodic linear differential equation

In this paper, we study the characteristic exponent for a second order linear differential equation x″+q(t)x=0x″+q(t)x=0 if q(t)<0q(t)<0. As an application, we calculate the characteristic exponents of Eq. x″+q(t)x=0x″+q(t)x=0 when q(t)<0q(t)<0. The obtained results can be seen as a good generalization of Shi and coworkers [3] and [4]. We end this paper with some examples which show the simplicity and the high accuracy of our result.